Deep Extreme Learning Machines Based Two-Phase Spatiotemporal Modeling for Distributed Parameter Systems

Xu, Kangkang

doi:10.1109/TII.2022.3165870

Deep Extreme Learning Machines Based Two-Phase Spatiotemporal Modeling for Distributed Parameter Systems

2023-03-01

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AI

DOI：10.1109/TII.2022.3165870

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Accurate and robust modeling of complex distributed parameter systems (DPSs) is a challenge for three reasons: 1) they have infinite-dimensional characteristics; 2) they are time/space coupled; and 3) there are model uncertainties. In this article, a two-phase spatiotemporal (S/T) modeling framework based on deep extreme learning machine (DELM) is proposed for DPSs. The modeling process consists of two S/T models in two phases: Phase I: a DELM model and Phase II: a Karhunen-Loeve (KL) based ELM (KL-ELM) model. In phase I, the DELM model is constructed by combing the multilayer ELM (ML-ELM), ELM, and kernel-based ELM (K-ELM) to approximate the dominant S/T dynamics of DPSs. Since DPSs have an infinite-dimensional characteristic that can hardly be handled directly, ML-ELM is first employed to transform the infinite-dimensional systems into finite-dimensional systems. Then, the ELM model is adopted to further approximate the finite-dimensional systems to ensure the model can predict future dynamic behavior. Finally, the K-ELM is used to reconstruct the infinite-dimensional systems, which can be considered as the inverse process of ML-ELM. Thus, the final DELM model can be used for prediction in both space and time directions. In phase II, a KL-ELM model is constructed to compensate for modeling errors caused by reconstruction error or unknown nonlinear dynamics. By integrating the obtained DELM and KL-ELM models, the proposed two-phase S/T model can be constructed. Experiments on a typical industrial thermal process verified that the proposed method may work better in complex DPSs.

Keywords:

Mathematical models

Computational modeling

Predictive models

Reduced order systems

Nonlinear dynamical systems

Nonhomogeneous media

Heuristic algorithms

Distributed parameter system (DPS)

Karhunen-Loeve (KL)

multilayer extreme learning machine (ML-ELM)

spatial basis functions (SBFs)

spatiotemporal (S/T) modeling

Deep Extreme Learning Machines Based Two-Phase Spatiotemporal Modeling for Distributed Parameter Systems

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